Case 2: Tesla

Tesla manufactures cars in three plants and then ships them to four regions of the country as follows:

	Region 1	Region 2	Region 3	Region 4	Capacity
Plant 1	$131	$218	$266	$120	450
Plant 2	$250	$116	$263	$278	600
Plant 3	$178	$132	$122	$180	500
Demand	450	200	300	300

A plant's capacity is listed in the rightmost column, while a regions demand is represented in the bottom

row. The unit costs to ship one vehicle from each plant to each region are listed in the middle.

Part A. Develop an LP optimization model that finds the cheapest way of shipping the automobiles from

the plants to the regions that stays within the plant's capacities while also meeting regional demands.

Part B. Elon Musk would like to extend the capabilities of the initial baseline model to more closely reflect the specifics of the actual situation. Since unit production costs vary from plant to plant, and the selling prices vary across the regions, there are different after tax profit implications associated with where the car is produced and sold, and where it is ultimately shipped to.

	Unit Production Cost	Tax Rate
Plant 1	$14,350	30%
Plant 2	$16,270	35%
Plant 3	$16,940	22%

	Unit Selling Price
Region 1	$19,290
Region 2	$20,520
Region 3	$17,570
Region 4	$18,320

For example, if Plant 1 produces an auto and ships it to Region 2, the before tax profit will be the unit's selling price in the Region, less the production costs from the Plant, less the shipping costs from the Plant to the Region (= $20,520 - $14,350 - $218 = $5,952). Since it was produced at Plant 1, the applicable after-tax profit would be; $5,952*(1-30%) = $4,166.40

Enhance the previous Model from Part A to consider the objective of maximizing after-tax profits. How does the enhancement of the model impact the solution recommendations.